The tube is very safe, the only issue you may have is being pickpocketed. That is different from being mugged as you don't even know about it, so you won't be traumatised by it, but you still won't have any stuff!! Make sure you keep your valuables hidden away, especially if your travelling at a busy time, you will be in crowds so not even feel someone dipping you. I don't know what sort of bag you have but across the body ones are good you can wear in under your coat, and have your money etc in and so be no danger of loosing the important stuff. Lots of people make the mistake of putting it in their rucksack, which is easy to open for others.
Apart from that, the underground is very safe. There are lots of underground "attendants" even when its quiet, and there are always people using the tube. (Next week is half term so there will be lots of kids out and about with parents, and they us the tube just aftet rush hour etc). Also at busy stations like Paddington, and King Cross (?) they do have police, but that's just really for show. Its not because its common for people to be hurt, attacked or mugged on the tube.
In that part of London, again it is very busy, and there are lots of people walking about, so it is highly unlikely you would be attacked simply walking along the street. Many many tourists/visitors make the transition to Paddington, so you'll just be one of the crowd. It sounds silly but London is very safe, you in a well populated "ordinary" area, not a rough one, and your not alone or there at the dead of night. Mothers do worry, but like you have said, many people make the journey every day, and you will be one of them.